Problem: Discuss steps for calculating compound interest for quarterly compounding. 1. State the problem and define variables. Define the principal $P$, the annual nominal interest rate $r$ expressed as a decimal, the number of compounding periods per year $n$, and the time in years $t$. For quarterly compounding set $n=4$. 2. Write the compound interest formula. The accumulated amount after $t$ years is given by the formula $$A = P\left(1 + \frac{r}{n}\right)^{nt}$$ For quarterly compounding substitute $n=4$ to get $$A = P\left(1 + \frac{r}{4}\right)^{4t}$$ 3. Calculation procedure. Given values for $P$, $r$, and $t$ compute step by step: first compute $r/4$, then compute $4t$, then compute the base $1+r/4$, raise it to the power $4t$, and finally multiply by $P$. 4. Worked numerical example. Let $P=1000$, $r=0.05$, and $t=3$. Compute $r/4=0.0125$. Compute $4t=12$. Compute base $1+0.0125=1.0125$. Compute $1.0125^{12}\approx1.16075$. Multiply by $P$ to obtain $A\approx1000\times1.16075=1160.75$. 5. Interpretation and tips. The investment grows to about 1160.75 after 3 years with quarterly compounding at 5 percent. For greater accuracy use a calculator or software to evaluate the power directly. If the rate is given as a percentage convert it to decimal by dividing by 100 before substituting into the formula. Final answer: The general formula for quarterly compounding is $$A = P\left(1 + \frac{r}{4}\right)^{4t}$$ and the worked example gives $A\approx1160.75$.